Tactile navigation

Introduction

A study on driving performance and In Vehicle infotainment system has been done. The study aims two answer two questions. 1) Can the addition of tactile navigation improve driving performance 2) Which tactile navigation (if any) improves driving performance most

The first part of this statistical analysis aims to investigate the sample to answer if the data is normally distributed and if the participants’s characteristics are distributed across the four conditions. If this is not the case an effect of condition could be attributed to other personal factors of the participants (e.g. gaming experience).

Dependent variables:
- SUS
- SART
- Total Crash
- Lane Breaks
- Total Glances
- Total Glance Time

Independent variable:
- Condition (Acrylic, Bar, Combination & Touch only)

Demographics:
- Gender
- Gaming
- Drivers licence Years
- Automatic gear experience
- Car Simulator

Population

A summary of ‘Age’ and ‘Years with drivers licence’. As with the bar graph for age we have a lot of people between 20-23 and most participants have had a drivers licence for 3-5 years.

##       Age       YearDriversLicence
##  Min.   :20.0   Min.   : 1.833    
##  1st Qu.:21.0   1st Qu.: 3.479    
##  Median :22.0   Median : 4.417    
##  Mean   :22.7   Mean   : 4.778    
##  3rd Qu.:23.0   3rd Qu.: 5.417    
##  Max.   :34.0   Max.   :16.000

## [1] 2.575191

## [1] 2.418032

Effect due to condition

To answer the first question of whether condition have an effect on the 6 metrics we’ll create a plot of means with confidence (95%) as whiskers. According to Geoff Cumming and Sue Finch if the data has the same standard deviation it is possible to gain insight into which data could be significantly different.

Plot of means Condition/metric

##     Condition  N      SUS       sd       se       ci
## 1     Acrylic 11 80.68182 11.12940 3.355642 7.476835
## 2         Bar 11 80.90909 11.36182 3.425717 7.632973
## 3 Combination 11 80.45455 12.23817 3.689946 8.221712
## 4  Touch_only 11 75.00000 14.23025 4.290582 9.560012

##     Condition  N     SART       sd       se       ci
## 1     Acrylic 11 15.00000 5.253570 1.584011 3.529396
## 2         Bar 11 14.72727 3.951985 1.191568 2.654979
## 3 Combination 11 14.54545 3.643175 1.098459 2.447519
## 4  Touch_only 11 14.00000 4.427189 1.334848 2.974226

##     Condition  N Total_crash        sd        se        ci
## 1     Acrylic 11   0.5454545 0.9341987 0.2816715 0.6276032
## 2         Bar 11   0.6363636 0.8090398 0.2439347 0.5435204
## 3 Combination 11   0.4545455 0.5222330 0.1574592 0.3508409
## 4  Touch_only 11   0.5454545 0.9341987 0.2816715 0.6276032

##     Condition  N Lane_Breaks       sd        se       ci
## 1     Acrylic 11    3.636364 3.074824 0.9270945 2.065695
## 2         Bar 11    4.454545 4.590504 1.3840890 3.083943
## 3 Combination 11    3.909091 2.625054 0.7914836 1.763535
## 4  Touch_only 11    3.818182 2.750207 0.8292185 1.847614

##     Condition  N Total_Glances        sd       se       ci
## 1     Acrylic 11      45.27273 12.042350 3.630905 8.090160
## 2         Bar 11      47.18182  6.274045 1.891696 4.214961
## 3 Combination 11      55.00000 13.798551 4.160420 9.269992
## 4  Touch_only 11      45.27273  7.156688 2.157823 4.807928

##     Condition  N Total_Glance_time        sd       se       ci
## 1     Acrylic 11          34.18545 10.471866 3.157387 7.035096
## 2         Bar 11          34.71636  7.799066 2.351507 5.239484
## 3 Combination 11          40.01091 10.989521 3.313465 7.382861
## 4  Touch_only 11          38.80273 10.009391 3.017945 6.724400

To test significance we will use ANOVA
ANOVA has Three assumptions
1) Normality
2) Homogenity
3) Independence
The assumption of Independence is meet as our participants haven’t influence each other in any way we know of. The participants were instructed not to speak with each other between trials and we can hope they have met this instruction.

Test of normality - Condition/metric

Cond1 <- subset(SartSusDemo, SartSusDemo$Condition=='Combination')
Cond2 <- subset(SartSusDemo, SartSusDemo$Condition=='Touch_only')
Cond3 <- subset(SartSusDemo, SartSusDemo$Condition=='Bar')
Cond4 <- subset(SartSusDemo, SartSusDemo$Condition=='Acrylic')

  shapiro.test(Cond1$SUS)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond1$SUS
## W = 0.73925, p-value = 0.001505

  shapiro.test(Cond2$SUS)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond2$SUS
## W = 0.91515, p-value = 0.2803

  shapiro.test(Cond3$SUS)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond3$SUS
## W = 0.92941, p-value = 0.4049

  shapiro.test(Cond4$SUS)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond4$SUS
## W = 0.87781, p-value = 0.09759

  shapiro.test(Cond1$SART)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond1$SART
## W = 0.92912, p-value = 0.4021

  shapiro.test(Cond2$SART)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond2$SART
## W = 0.83396, p-value = 0.02632

  shapiro.test(Cond3$SART)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond3$SART
## W = 0.96283, p-value = 0.8064

  shapiro.test(Cond4$SART)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond4$SART
## W = 0.98203, p-value = 0.9764

  shapiro.test(Cond1$Total_Glance_time)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond1$Total_Glance_time
## W = 0.94149, p-value = 0.5381

  shapiro.test(Cond2$Total_Glance_time)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond2$Total_Glance_time
## W = 0.92679, p-value = 0.3793

  shapiro.test(Cond3$Total_Glance_time)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond3$Total_Glance_time
## W = 0.95557, p-value = 0.7155

  shapiro.test(Cond4$Total_Glance_time)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond4$Total_Glance_time
## W = 0.91494, p-value = 0.2787

  shapiro.test(Cond1$Total_Glances)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond1$Total_Glances
## W = 0.97154, p-value = 0.9016

  shapiro.test(Cond2$Total_Glances)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond2$Total_Glances
## W = 0.84398, p-value = 0.03561

  shapiro.test(Cond3$Total_Glances)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond3$Total_Glances
## W = 0.91694, p-value = 0.294

  shapiro.test(Cond4$Total_Glances)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond4$Total_Glances
## W = 0.94695, p-value = 0.6053

  shapiro.test(Cond1$Lane_Breaks)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond1$Lane_Breaks
## W = 0.95245, p-value = 0.6754

  shapiro.test(Cond2$Lane_Breaks)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond2$Lane_Breaks
## W = 0.95583, p-value = 0.7188

  shapiro.test(Cond3$Lane_Breaks)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond3$Lane_Breaks
## W = 0.84061, p-value = 0.03216

  shapiro.test(Cond4$Lane_Breaks)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond4$Lane_Breaks
## W = 0.90516, p-value = 0.2135

  shapiro.test(Cond1$Total_crash)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond1$Total_crash
## W = 0.64917, p-value = 0.0001052

  shapiro.test(Cond2$Total_crash)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond2$Total_crash
## W = 0.64952, p-value = 0.0001063

  shapiro.test(Cond3$Total_crash)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond3$Total_crash
## W = 0.75438, p-value = 0.002371

  shapiro.test(Cond4$Total_crash)

## 
##  Shapiro-Wilk normality test
## 
## data:  Cond4$Total_crash
## W = 0.64952, p-value = 0.0001063

There are 8 scores which break normality
Condition 1 - SUS (0.001505)
Condition 2 - SART (0.02632)
Condition 2 - Total Glances (0.03561)
Condition 3 - Lane breaks (0.03216)

Condition 1 - Total Crash (0.0001052)
Condition 2 - Total Crash (0.0001063)
Condition 3 - Total Crash (0.002371)
Condition 4 - Total Crash (0.0001063)

Another way to present the crash data would be to score crashes pr condition: It can be seen on this graph that each condition has about the same total crashes and some conditions have one or two participants responsible for extra crashes.

Test of homogeneity - Condition/metric

To test for homogeneity we’ll use Levines test for the scores which aren’t normally distributed and Bartletts test for the scores which are normally distributed.

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  3  0.2143 0.8859
##       40

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  3  0.4316 0.7315
##       40

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value  Pr(>F)  
## group  3  2.3109 0.09079 .
##       40                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Total_Glance_time by Condition
## Bartlett's K-squared = 1.2274, df = 3, p-value = 0.7464

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  3  0.0907 0.9647
##       40

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  3  0.4612 0.7109
##       40

We see that the variance in metrics across the four conditions are not significantly different.

Test significance

We now have two options
1) Compute an ANOVA because it is said to be somewhat robust against violations of normal distribution
2) Compute a Welsh ANOVA (it is robust against normal distribution but not unequal variance (heteroscedastic))
3) Compute a Kruskal-Wallis test - as our data has equal varience (homoscedasticity) but is not normally distributed

We will choose option 3) and compute the Kruskal-Wallis test

Note: Total Glance Time is both normally distributed and has homoscedasticity and therefore an anova can be computed

SUS <- kruskal.test(SUS ~ Condition, data = SartSusDemo)
SART <- kruskal.test(SART ~ Condition, data = SartSusDemo)
Glances <- kruskal.test(Total_Glances ~ Condition, data = SartSusDemo)
Crashes <- kruskal.test(Total_crash ~ Condition, data = SartSusDemo)
LaneBreaks <- kruskal.test(Lane_Breaks ~ Condition, data = SartSusDemo)
GlanceTime <- aov(Total_Glance_time ~ Condition, data = SartSusDemo, var.equal = TRUE)

SUS

## 
##  Kruskal-Wallis rank sum test
## 
## data:  SUS by Condition
## Kruskal-Wallis chi-squared = 1.973, df = 3, p-value = 0.578

SART

## 
##  Kruskal-Wallis rank sum test
## 
## data:  SART by Condition
## Kruskal-Wallis chi-squared = 0.23728, df = 3, p-value = 0.9714

Glances

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Total_Glances by Condition
## Kruskal-Wallis chi-squared = 4.2639, df = 3, p-value = 0.2343

Crashes

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Total_crash by Condition
## Kruskal-Wallis chi-squared = 0.32696, df = 3, p-value = 0.9549

LaneBreaks

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Lane_Breaks by Condition
## Kruskal-Wallis chi-squared = 0.23381, df = 3, p-value = 0.972

summary(GlanceTime)

##             Df Sum Sq Mean Sq F value Pr(>F)
## Condition    3    280   93.25   0.953  0.424
## Residuals   40   3914   97.86

None of the 6 metrics have significant differences between conditions

Plot of means - All Dependent variables vs All Independent variables

To investigate weather differences in demographics have had an influence on conditions a plot of means for each metric will be performed with each independent variable. This will be done with wiskers as 95% confidence interval and if the data has homoscedasticity it could be possible to eyeball significant influences. If these are detected we’ll perform a t-test

Dependent variables:
- SUS
- SART
- Total Crash
- Lane Breaks
- Total Glances
- Total Glance Time

Independent variables:
- Condition
- Gender
- Gaming
- Drivers licence (This plot will have a linear model underneath it (x=Years with drivers license y=Dependent variable)) - Automatic gear
- Car Simulator

SUS

  SaveSixPlots(Metric="SUS")

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## 
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## 
## Call:
## lm(formula = y ~ x, data = SartSusDemo)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -30.709  -5.248   3.083   9.022  16.419 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  81.9245     4.1078  19.944   <2e-16 ***
## x            -0.5573     0.7688  -0.725    0.473    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.19 on 42 degrees of freedom
## Multiple R-squared:  0.01236,    Adjusted R-squared:  -0.01116 
## F-statistic: 0.5255 on 1 and 42 DF,  p-value: 0.4725
## 
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Sart

  SaveSixPlots("SART")

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## 
## Call:
## lm(formula = y ~ x, data = SartSusDemo)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.1972  -2.7311   0.4113   2.7137  10.0469 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  15.8408     1.4230   11.13 4.15e-14 ***
## x            -0.2663     0.2663   -1.00    0.323    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.223 on 42 degrees of freedom
## Multiple R-squared:  0.02326,    Adjusted R-squared:  1.648e-06 
## F-statistic:     1 on 1 and 42 DF,  p-value: 0.323
## 
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### Total crash

  SaveSixPlots("Total_crash")

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## 
## Call:
## lm(formula = y ~ x, data = SartSusDemo)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.7467 -0.5342 -0.4567  0.4499  2.5671 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.31767    0.26684   1.190    0.241
## x            0.04767    0.04994   0.954    0.345
## 
## Residual standard error: 0.7919 on 42 degrees of freedom
## Multiple R-squared:  0.02123,    Adjusted R-squared:  -0.002073 
## F-statistic: 0.9111 on 1 and 42 DF,  p-value: 0.3453
## 
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Lane Breaks

  SaveSixPlots("Lane_Breaks")

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## 
## [[5]]
## 
## Call:
## lm(formula = y ~ x, data = SartSusDemo)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -4.543 -2.116 -0.846  1.936 11.433 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   3.2883     1.1018   2.985  0.00472 **
## x             0.1394     0.2062   0.676  0.50263   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.27 on 42 degrees of freedom
## Multiple R-squared:  0.01077,    Adjusted R-squared:  -0.01278 
## F-statistic: 0.4572 on 1 and 42 DF,  p-value: 0.5026
## 
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Total Glances

  SaveSixPlots("Total_Glances")

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## 
## Call:
## lm(formula = y ~ x, data = SartSusDemo)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -19.0630  -7.3500   0.1733   6.0047  31.5646 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  49.0715     3.6618  13.401   <2e-16 ***
## x            -0.1862     0.6853  -0.272    0.787    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.87 on 42 degrees of freedom
## Multiple R-squared:  0.001754,   Adjusted R-squared:  -0.02201 
## F-statistic: 0.0738 on 1 and 42 DF,  p-value: 0.7872
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### Total Glance time

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## 
## Call:
## lm(formula = y ~ x, data = SartSusDemo)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.2765  -8.3324   0.0377   5.3081  22.1420 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  38.4526     3.3570  11.454 1.67e-14 ***
## x            -0.3189     0.6283  -0.508    0.614    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.963 on 42 degrees of freedom
## Multiple R-squared:  0.006096,   Adjusted R-squared:  -0.01757 
## F-statistic: 0.2576 on 1 and 42 DF,  p-value: 0.6144
## 
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From the many plot of means with confidence interval 95% as wisksers we’ve determined to test the following interactions

LaneBreaksAutomatic  <- t.test(formula = Lane_Breaks ~ Automatic, data = SartSusDemo)
SartGender <- t.test(formula = SART ~ Gender, data = SartSusDemo)
CrashComputer <- kruskal.test(formula = Total_crash ~ ComputerGames, data = SartSusDemo)
CrashAutomatic <- t.test(formula = Total_crash ~ Automatic, data = SartSusDemo)
GlanceTimeAutomatic <- t.test(formula = Total_Glance_time ~ Automatic, data = SartSusDemo)
GlanceCondition <- kruskal.test(formula = Total_Glance_time ~ Condition, data = SartSusDemo)
GlancesGender <- t.test(formula = Total_Glances ~ Gender, data = SartSusDemo)
GlancesAutomatic <- t.test(formula = Total_Glances ~ Automatic, data = SartSusDemo)

#Måske er der noget med glances og condition
attach(SartSusDemo)
GlancesCondition <- pairwise.t.test(Total_Glances, Condition,p.adj = "bonf")
detach()

 LaneBreaksAutomatic

## 
##  Welch Two Sample t-test
## 
## data:  Lane_Breaks by Automatic
## t = 2.6531, df = 17.133, p-value = 0.01666
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.618242 5.406572
## sample estimates:
##  mean in group No mean in group Yes 
##          6.076923          3.064516

 SartGender

## 
##  Welch Two Sample t-test
## 
## data:  SART by Gender
## t = -2.4169, df = 17.261, p-value = 0.02699
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -5.9791715 -0.4090638
## sample estimates:
## mean in group F mean in group M 
##        12.10000        15.29412

 CrashComputer

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Total_crash by ComputerGames
## Kruskal-Wallis chi-squared = 2.116, df = 2, p-value = 0.3471

 CrashAutomatic

## 
##  Welch Two Sample t-test
## 
## data:  Total_crash by Automatic
## t = 1.9435, df = 13.821, p-value = 0.0726
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.06767813  1.35800071
## sample estimates:
##  mean in group No mean in group Yes 
##         1.0000000         0.3548387

 GlanceTimeAutomatic

## 
##  Welch Two Sample t-test
## 
## data:  Total_Glance_time by Automatic
## t = 2.953, df = 23.453, p-value = 0.007043
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   2.626666 14.871746
## sample estimates:
##  mean in group No mean in group Yes 
##          43.09308          34.34387

 GlanceCondition

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Total_Glance_time by Condition
## Kruskal-Wallis chi-squared = 2.4534, df = 3, p-value = 0.4838

 GlancesGender

## 
##  Welch Two Sample t-test
## 
## data:  Total_Glances by Gender
## t = 1.8374, df = 24.153, p-value = 0.07848
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.6707051 11.5883521
## sample estimates:
## mean in group F mean in group M 
##        52.40000        46.94118

 GlancesAutomatic

## 
##  Welch Two Sample t-test
## 
## data:  Total_Glances by Automatic
## t = 1.8943, df = 20.358, p-value = 0.07249
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.6836275 14.3610468
## sample estimates:
##  mean in group No mean in group Yes 
##          53.00000          46.16129

 GlancesCondition

## 
##  Pairwise comparisons using t tests with pooled SD 
## 
## data:  Total_Glances and Condition 
## 
##             Acrylic Bar Combination
## Bar         1.0     -   -          
## Combination 0.2     0.5 -          
## Touch_only  1.0     1.0 0.2        
## 
## P value adjustment method: bonferroni

When analysing this much data the risk of p-hacking increases. We’ll only use these significanses if there is a big heteroscedasticity in regards to the four conditions maybe this change can explain

The four significant effects were:
1) Lane_Breaks by Automatic 0.01666
2) Total_Glance_time by Automatic 0.007043

AutomaticExperienceCondition

Automatic experience is distributed quite nice with a difference of 2 between highest and lowest. Therefore this effect is irrelevant.
3) SART by Gender 0.02699

GenderCondition

Gender is distributed with a difference of 1 between highest and lowest. Therefore this effect is irrelevant